A343424 Numbers k such that sopfr((k-1)!) is divisible by k, where sopfr(k) = A001414(k) = sum of primes, with repetition, dividing k.

1, 2, 45, 53, 177, 436, 1239, 3651, 6463, 6869, 10753, 19450, 29721, 33289, 88907, 93682, 1137232, 1516121, 4361271, 9428534, 43778664, 74738670, 271442366, 775223371, 835126289, 1736463189, 3088442241, 5054888590, 11184483614, 16993011938, 30788570768, 33342871740

Offset

1,2

Comments

See A025281(k-1) for the values of sopfr((k-1)!).

Links

Martin Ehrenstein, Table of n, a(n) for n = 1..35

Example

45 is a term as sopfr(44!) = 585 which is divisible by 45.

Mathematica

sopfr[0] = sopfr[1] = 0; sopfr[n_] := Plus @@ Times @@@ FactorInteger[n]; sum = 0; s = {}; Do[sum += sopfr[n]; If[Divisible[sum, n + 1], AppendTo[s, n + 1]], {n, 0, 10^6}]; s (* Amiram Eldar, May 06 2021 *)

Prog

(PARI) sopfr(n) = (n=factor(n))[, 1]~*n[, 2]; \\ A001414
isok(k) = !(sopfr((k-1)!) % k); \\ Michel Marcus, May 06 2021

Crossrefs

Cf. A001414, A025281, A027746.

Sequence in context: A342827 A264438 A241762 * A041241 A304015 A279680

Adjacent sequences: A343421 A343422 A343423 * A343425 A343426 A343427

Keyword

nonn

Author

Scott R. Shannon, Apr 15 2021

Extensions

a(27) from Amiram Eldar, May 06 2021

a(28) and beyond from Martin Ehrenstein, May 16 2021

Status

approved